\documentclass[9pt]{article}
\usepackage{amsmath}
\begin{document}
Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  -11.0 & + 10.00 x_{1} & -9.00 x_{2} & +  6.00 x_{3} & -1.00 x_{4} & -6.00 x_{5} & -3.00 x_{6} & +  9.00 x_{7} & -2.00 x_{8}\\
 x_{10}   &  -1.0 & +  5.00 x_{1} & +  2.00 x_{2} & +  8.00 x_{3} & +  4.00 x_{4} & -6.00 x_{5} & -3.00 x_{6} & -2.00 x_{7} & -8.00 x_{8}\\
 x_{11}   &  27.0  &   & -8.00 x_{2} & -9.00 x_{3} & +  7.00 x_{4} & + 10.00 x_{5} & -2.00 x_{6} &   & -5.00 x_{8}\\
 x_{12}   &  42.0 & +  8.00 x_{1} & -4.00 x_{2} & -10.00 x_{3} & -8.00 x_{4} & +  6.00 x_{5} & -9.00 x_{6} & +  2.00 x_{7} & -10.00 x_{8}\\
 x_{13}   &  7.0 & -9.00 x_{1} & -6.00 x_{2} & +  1.00 x_{3} & +  7.00 x_{4} & +  5.00 x_{5} &   & -2.00 x_{7} & +  6.00 x_{8}\\
 x_{14}   &  34.0 & -9.00 x_{1} & -5.00 x_{2} & -5.00 x_{3} & +  1.00 x_{4} & + 10.00 x_{5} & -2.00 x_{6} & +  1.00 x_{7} & -10.00 x_{8}\\
 x_{15}   &  8.0 & +  5.00 x_{1} & -3.00 x_{2} & -10.00 x_{3} & +  9.00 x_{4} & +  4.00 x_{5} & +  5.00 x_{6} & -9.00 x_{7} & +  8.00 x_{8}\\
 x_{16}   &  19.0 & -6.00 x_{1} & +  3.00 x_{2} & +  3.00 x_{3} & +  6.00 x_{4} & -4.00 x_{5} & -6.00 x_{6} & -3.00 x_{7} & -4.00 x_{8}\\
\hline
z    &  0.0 & -4.00 x_{1} & +  1.00 x_{2} &   & +  5.00 x_{4} & -2.00 x_{5} & -1.00 x_{6} & +  5.00 x_{7} &   \\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{8}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,16$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & -10.00 y_{9} & -5.00 y_{10} &   & -8.00 y_{12} & +  9.00 y_{13} & +  9.00 y_{14} & -5.00 y_{15} & +  6.00 y_{16}\\
 y_{2}   &  1.0 & +  9.00 y_{9} & -2.00 y_{10} & +  8.00 y_{11} & +  4.00 y_{12} & +  6.00 y_{13} & +  5.00 y_{14} & +  3.00 y_{15} & -3.00 y_{16}\\
 y_{3}   &  1.0 & -6.00 y_{9} & -8.00 y_{10} & +  9.00 y_{11} & + 10.00 y_{12} & -1.00 y_{13} & +  5.00 y_{14} & + 10.00 y_{15} & -3.00 y_{16}\\
 y_{4}   &  1.0 & +  1.00 y_{9} & -4.00 y_{10} & -7.00 y_{11} & +  8.00 y_{12} & -7.00 y_{13} & -1.00 y_{14} & -9.00 y_{15} & -6.00 y_{16}\\
 y_{5}   &  1.0 & +  6.00 y_{9} & +  6.00 y_{10} & -10.00 y_{11} & -6.00 y_{12} & -5.00 y_{13} & -10.00 y_{14} & -4.00 y_{15} & +  4.00 y_{16}\\
 y_{6}   &  1.0 & +  3.00 y_{9} & +  3.00 y_{10} & +  2.00 y_{11} & +  9.00 y_{12} &   & +  2.00 y_{14} & -5.00 y_{15} & +  6.00 y_{16}\\
 y_{7}   &  1.0 & -9.00 y_{9} & +  2.00 y_{10} &   & -2.00 y_{12} & +  2.00 y_{13} & -1.00 y_{14} & +  9.00 y_{15} & +  3.00 y_{16}\\
 y_{8}   &  1.0 & +  2.00 y_{9} & +  8.00 y_{10} & +  5.00 y_{11} & + 10.00 y_{12} & -6.00 y_{13} & + 10.00 y_{14} & -8.00 y_{15} & +  4.00 y_{16}\\
\hline
z    &  -0 & + 11.00 y_{9} & +  1.00 y_{10} & -27.00 y_{11} & -42.00 y_{12} & -7.00 y_{13} & -34.00 y_{14} & -8.00 y_{15} & -19.00 y_{16}\\
\end{array}\]
Initialization succeeded in finding final dual dictionary with 3 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{9}   &  0.114754098361 & +  0.03 y_{1} & +  0.46 y_{10} &   & -0.03 y_{12} & -0.15 y_{7} & -0.44 y_{14} & +  1.49 y_{15} & +  0.25 y_{16}\\
 y_{2}   &  2.13114754098 & +  1.18 y_{1} & +  8.52 y_{10} & +  8.00 y_{11} & +  8.82 y_{12} & -2.31 y_{7} & -7.93 y_{14} & + 29.70 y_{15} & -3.15 y_{16}\\
 y_{3}   &  0.295081967213 & -0.34 y_{1} & -11.82 y_{10} & +  9.00 y_{11} & +  9.34 y_{12} & +  1.05 y_{7} & +  9.15 y_{14} & -1.16 y_{15} & -4.08 y_{16}\\
 y_{4}   &  1.0 & -1.00 y_{1} & -11.00 y_{10} & -7.00 y_{11} & +  2.00 y_{12} & +  1.00 y_{7} & +  9.00 y_{14} & -23.00 y_{15} & -3.00 y_{16}\\
 y_{5}   &  1.60655737705 & -0.54 y_{1} & +  3.43 y_{10} & -10.00 y_{11} & -10.46 y_{12} & -0.07 y_{7} & -5.20 y_{14} & -6.11 y_{15} & +  7.44 y_{16}\\
 y_{6}   &  1.34426229508 & +  0.10 y_{1} & +  4.38 y_{10} & +  2.00 y_{11} & +  8.90 y_{12} & -0.44 y_{7} & +  0.67 y_{14} & -0.52 y_{15} & +  6.74 y_{16}\\
 y_{13}   &  0.016393442623 & +  0.15 y_{1} & +  1.07 y_{10} &   & +  0.85 y_{12} & -0.16 y_{7} & -1.49 y_{14} & +  2.21 y_{15} & -0.39 y_{16}\\
 y_{8}   &  1.13114754098 & -0.82 y_{1} & +  2.52 y_{10} & +  5.00 y_{11} & +  4.82 y_{12} & +  0.69 y_{7} & + 18.07 y_{14} & -18.30 y_{15} & +  6.85 y_{16}\\
\hline
z    &  1.14754098361 & -0.67 y_{1} & -1.41 y_{10} & -27.00 y_{11} & -48.33 y_{12} & -0.48 y_{7} & -28.43 y_{14} & -7.08 y_{15} & -13.54 y_{16}\\
\end{array}\]
Primal Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{1}   &  0.672131147541 & -0.03 x_{9} & -1.18 x_{2} & +  0.34 x_{3} & +  1.00 x_{4} & +  0.54 x_{5} & -0.10 x_{6} & -0.15 x_{13} & +  0.82 x_{8}\\
 x_{10}   &  1.40983606557 & -0.46 x_{9} & -8.52 x_{2} & + 11.82 x_{3} & + 11.00 x_{4} & -3.43 x_{5} & -4.38 x_{6} & -1.07 x_{13} & -2.52 x_{8}\\
 x_{11}   &  27.0  &   & -8.00 x_{2} & -9.00 x_{3} & +  7.00 x_{4} & + 10.00 x_{5} & -2.00 x_{6} &   & -5.00 x_{8}\\
 x_{12}   &  48.3278688525 & +  0.03 x_{9} & -8.82 x_{2} & -9.34 x_{3} & -2.00 x_{4} & + 10.46 x_{5} & -8.90 x_{6} & -0.85 x_{13} & -4.82 x_{8}\\
 x_{7}   &  0.475409836066 & +  0.15 x_{9} & +  2.31 x_{2} & -1.05 x_{3} & -1.00 x_{4} & +  0.07 x_{5} & +  0.44 x_{6} & +  0.16 x_{13} & -0.69 x_{8}\\
 x_{14}   &  28.4262295082 & +  0.44 x_{9} & +  7.93 x_{2} & -9.15 x_{3} & -9.00 x_{4} & +  5.20 x_{5} & -0.67 x_{6} & +  1.49 x_{13} & -18.07 x_{8}\\
 x_{15}   &  7.08196721311 & -1.49 x_{9} & -29.70 x_{2} & +  1.16 x_{3} & + 23.00 x_{4} & +  6.11 x_{5} & +  0.52 x_{6} & -2.21 x_{13} & + 18.30 x_{8}\\
 x_{16}   &  13.5409836066 & -0.25 x_{9} & +  3.15 x_{2} & +  4.08 x_{3} & +  3.00 x_{4} & -7.44 x_{5} & -6.74 x_{6} & +  0.39 x_{13} & -6.85 x_{8}\\
\hline
z    &  -1.14754098361 & -0.11 x_{9} & -2.13 x_{2} & -0.30 x_{3} & -1.00 x_{4} & -1.61 x_{5} & -1.34 x_{6} & -0.02 x_{13} & -1.13 x_{8}\\
\end{array}\]
Primal Dictionary with original objective is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{1}   &  0.672131147541 & -0.03 x_{9} & -1.18 x_{2} & +  0.34 x_{3} & +  1.00 x_{4} & +  0.54 x_{5} & -0.10 x_{6} & -0.15 x_{13} & +  0.82 x_{8}\\
 x_{10}   &  1.40983606557 & -0.46 x_{9} & -8.52 x_{2} & + 11.82 x_{3} & + 11.00 x_{4} & -3.43 x_{5} & -4.38 x_{6} & -1.07 x_{13} & -2.52 x_{8}\\
 x_{11}   &  27.0  &   & -8.00 x_{2} & -9.00 x_{3} & +  7.00 x_{4} & + 10.00 x_{5} & -2.00 x_{6} &   & -5.00 x_{8}\\
 x_{12}   &  48.3278688525 & +  0.03 x_{9} & -8.82 x_{2} & -9.34 x_{3} & -2.00 x_{4} & + 10.46 x_{5} & -8.90 x_{6} & -0.85 x_{13} & -4.82 x_{8}\\
 x_{7}   &  0.475409836066 & +  0.15 x_{9} & +  2.31 x_{2} & -1.05 x_{3} & -1.00 x_{4} & +  0.07 x_{5} & +  0.44 x_{6} & +  0.16 x_{13} & -0.69 x_{8}\\
 x_{14}   &  28.4262295082 & +  0.44 x_{9} & +  7.93 x_{2} & -9.15 x_{3} & -9.00 x_{4} & +  5.20 x_{5} & -0.67 x_{6} & +  1.49 x_{13} & -18.07 x_{8}\\
 x_{15}   &  7.08196721311 & -1.49 x_{9} & -29.70 x_{2} & +  1.16 x_{3} & + 23.00 x_{4} & +  6.11 x_{5} & +  0.52 x_{6} & -2.21 x_{13} & + 18.30 x_{8}\\
 x_{16}   &  13.5409836066 & -0.25 x_{9} & +  3.15 x_{2} & +  4.08 x_{3} & +  3.00 x_{4} & -7.44 x_{5} & -6.74 x_{6} & +  0.39 x_{13} & -6.85 x_{8}\\
\hline
z    &  -0.311475409836 & +  0.87 x_{9} & + 17.28 x_{2} & -6.62 x_{3} & -4.00 x_{4} & -3.84 x_{5} & +  1.61 x_{6} & +  1.41 x_{13} & -6.72 x_{8}\\
\end{array}\]
\section{Optimization Phase Simplex}
Starting Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{1}   &  0.672131147541 & -0.03 x_{9} & -1.18 x_{2} & +  0.34 x_{3} & +  1.00 x_{4} & +  0.54 x_{5} & -0.10 x_{6} & -0.15 x_{13} & +  0.82 x_{8}\\
 x_{10}   &  1.40983606557 & -0.46 x_{9} & -8.52 x_{2} & + 11.82 x_{3} & + 11.00 x_{4} & -3.43 x_{5} & -4.38 x_{6} & -1.07 x_{13} & -2.52 x_{8}\\
 x_{11}   &  27.0  &   & -8.00 x_{2} & -9.00 x_{3} & +  7.00 x_{4} & + 10.00 x_{5} & -2.00 x_{6} &   & -5.00 x_{8}\\
 x_{12}   &  48.3278688525 & +  0.03 x_{9} & -8.82 x_{2} & -9.34 x_{3} & -2.00 x_{4} & + 10.46 x_{5} & -8.90 x_{6} & -0.85 x_{13} & -4.82 x_{8}\\
 x_{7}   &  0.475409836066 & +  0.15 x_{9} & +  2.31 x_{2} & -1.05 x_{3} & -1.00 x_{4} & +  0.07 x_{5} & +  0.44 x_{6} & +  0.16 x_{13} & -0.69 x_{8}\\
 x_{14}   &  28.4262295082 & +  0.44 x_{9} & +  7.93 x_{2} & -9.15 x_{3} & -9.00 x_{4} & +  5.20 x_{5} & -0.67 x_{6} & +  1.49 x_{13} & -18.07 x_{8}\\
 x_{15}   &  7.08196721311 & -1.49 x_{9} & -29.70 x_{2} & +  1.16 x_{3} & + 23.00 x_{4} & +  6.11 x_{5} & +  0.52 x_{6} & -2.21 x_{13} & + 18.30 x_{8}\\
 x_{16}   &  13.5409836066 & -0.25 x_{9} & +  3.15 x_{2} & +  4.08 x_{3} & +  3.00 x_{4} & -7.44 x_{5} & -6.74 x_{6} & +  0.39 x_{13} & -6.85 x_{8}\\
\hline
z    &  -0.311475409836 & +  0.87 x_{9} & + 17.28 x_{2} & -6.62 x_{3} & -4.00 x_{4} & -3.84 x_{5} & +  1.61 x_{6} & +  1.41 x_{13} & -6.72 x_{8}\\
\end{array}\]


 $ x_{2} $ enters and $ x_{10} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{1}   &  0.476923076923 & +  0.03 x_{9} & +  0.14 x_{10} & -1.29 x_{3} & -0.52 x_{4} & +  1.02 x_{5} & +  0.51 x_{6} & +  0.00 x_{13} & +  1.17 x_{8}\\
 x_{2}   &  0.165384615385 & -0.05 x_{9} & -0.12 x_{10} & +  1.39 x_{3} & +  1.29 x_{4} & -0.40 x_{5} & -0.51 x_{6} & -0.12 x_{13} & -0.30 x_{8}\\
 x_{11}   &  25.6769230769 & +  0.43 x_{9} & +  0.94 x_{10} & -20.09 x_{3} & -3.32 x_{4} & + 13.22 x_{5} & +  2.11 x_{6} & +  1.00 x_{13} & -2.63 x_{8}\\
 x_{12}   &  46.8692307692 & +  0.51 x_{9} & +  1.03 x_{10} & -21.57 x_{3} & -13.38 x_{4} & + 14.00 x_{5} & -4.37 x_{6} & +  0.25 x_{13} & -2.21 x_{8}\\
 x_{7}   &  0.857692307692 & +  0.02 x_{9} & -0.27 x_{10} & +  2.16 x_{3} & +  1.98 x_{4} & -0.86 x_{5} & -0.74 x_{6} & -0.12 x_{13} & -1.37 x_{8}\\
 x_{14}   &  29.7384615385 & +  0.02 x_{9} & -0.93 x_{10} & +  1.85 x_{3} & +  1.24 x_{4} & +  2.01 x_{5} & -4.75 x_{6} & +  0.50 x_{13} & -20.42 x_{8}\\
 x_{15}   &  2.16923076923 & +  0.11 x_{9} & +  3.48 x_{10} & -40.02 x_{3} & -15.33 x_{4} & + 18.05 x_{5} & + 15.78 x_{6} & +  1.50 x_{13} & + 27.09 x_{8}\\
 x_{16}   &  14.0615384615 & -0.42 x_{9} & -0.37 x_{10} & +  8.45 x_{3} & +  7.06 x_{4} & -8.71 x_{5} & -8.35 x_{6} & -0.00 x_{13} & -7.78 x_{8}\\
\hline
z    &  2.54615384615 & -0.06 x_{9} & -2.03 x_{10} & + 17.33 x_{3} & + 18.30 x_{4} & -10.78 x_{5} & -7.27 x_{6} & -0.75 x_{13} & -11.84 x_{8}\\
\end{array}\]


 $ x_{3} $ enters and $ x_{15} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{1}   &  0.406880645781 & +  0.03 x_{9} & +  0.03 x_{10} & +  0.03 x_{15} & -0.03 x_{4} & +  0.43 x_{5} & -0.00 x_{6} & -0.05 x_{13} & +  0.29 x_{8}\\
 x_{2}   &  0.240534307131 & -0.05 x_{9} & +  0.00 x_{10} & -0.03 x_{15} & +  0.76 x_{4} & +  0.22 x_{5} & +  0.03 x_{6} & -0.07 x_{13} & +  0.64 x_{8}\\
 x_{11}   &  24.5879300404 & +  0.38 x_{9} & -0.81 x_{10} & +  0.50 x_{15} & +  4.37 x_{4} & +  4.15 x_{5} & -5.81 x_{6} & +  0.25 x_{13} & -16.23 x_{8}\\
 x_{12}   &  45.6999807803 & +  0.45 x_{9} & -0.84 x_{10} & +  0.54 x_{15} & -5.12 x_{4} & +  4.27 x_{5} & -12.88 x_{6} & -0.56 x_{13} & -16.81 x_{8}\\
 x_{7}   &  0.974533922737 & +  0.03 x_{9} & -0.08 x_{10} & -0.05 x_{15} & +  1.16 x_{4} & +  0.11 x_{5} & +  0.11 x_{6} & -0.04 x_{13} & +  0.09 x_{8}\\
 x_{14}   &  29.8389390736 & +  0.02 x_{9} & -0.77 x_{10} & -0.05 x_{15} & +  0.53 x_{4} & +  2.84 x_{5} & -4.02 x_{6} & +  0.57 x_{13} & -19.16 x_{8}\\
 x_{3}   &  0.0541995002883 & +  0.00 x_{9} & +  0.09 x_{10} & -0.02 x_{15} & -0.38 x_{4} & +  0.45 x_{5} & +  0.39 x_{6} & +  0.04 x_{13} & +  0.68 x_{8}\\
 x_{16}   &  14.5193157794 & -0.39 x_{9} & +  0.37 x_{10} & -0.21 x_{15} & +  3.83 x_{4} & -4.90 x_{5} & -5.02 x_{6} & +  0.32 x_{13} & -2.07 x_{8}\\
\hline
z    &  3.48568133769 & -0.01 x_{9} & -0.52 x_{10} & -0.43 x_{15} & + 11.66 x_{4} & -2.96 x_{5} & -0.43 x_{6} & -0.10 x_{13} & -0.10 x_{8}\\
\end{array}\]


 $ x_{4} $ enters and $ x_{3} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{1}   &  0.40291018565 & +  0.03 x_{9} & +  0.02 x_{10} & +  0.03 x_{15} & +  0.07 x_{3} & +  0.40 x_{5} & -0.03 x_{6} & -0.05 x_{13} & +  0.24 x_{8}\\
 x_{2}   &  0.347967887607 & -0.04 x_{9} & +  0.18 x_{10} & -0.08 x_{15} & -1.98 x_{3} & +  1.12 x_{5} & +  0.81 x_{6} & +  0.00 x_{13} & +  1.98 x_{8}\\
 x_{11}   &  25.2067235324 & +  0.41 x_{9} & +  0.18 x_{10} & +  0.22 x_{15} & -11.42 x_{3} & +  9.30 x_{5} & -1.31 x_{6} & +  0.67 x_{13} & -8.50 x_{8}\\
 x_{12}   &  44.975915705 & +  0.41 x_{9} & -2.01 x_{10} & +  0.87 x_{15} & + 13.36 x_{3} & -1.75 x_{5} & -18.14 x_{6} & -1.06 x_{13} & -25.85 x_{8}\\
 x_{7}   &  1.13823381836 & +  0.04 x_{9} & +  0.18 x_{10} & -0.13 x_{15} & -3.02 x_{3} & +  1.47 x_{5} & +  1.30 x_{6} & +  0.07 x_{13} & +  2.13 x_{8}\\
 x_{14}   &  29.9136979428 & +  0.02 x_{9} & -0.65 x_{10} & -0.08 x_{15} & -1.38 x_{3} & +  3.47 x_{5} & -3.47 x_{6} & +  0.62 x_{13} & -18.23 x_{8}\\
 x_{4}   &  0.141495233317 & +  0.01 x_{9} & +  0.23 x_{10} & -0.07 x_{15} & -2.61 x_{3} & +  1.18 x_{5} & +  1.03 x_{6} & +  0.10 x_{13} & +  1.77 x_{8}\\
 x_{16}   &  15.0607124937 & -0.37 x_{9} & +  1.24 x_{10} & -0.46 x_{15} & -9.99 x_{3} & -0.39 x_{5} & -1.09 x_{6} & +  0.69 x_{13} & +  4.69 x_{8}\\
\hline
z    &  5.13497240341 & +  0.07 x_{9} & +  2.13 x_{10} & -1.19 x_{15} & -30.43 x_{3} & + 10.77 x_{5} & + 11.56 x_{6} & +  1.04 x_{13} & + 20.49 x_{8}\\
\end{array}\]


 $ x_{5} $ enters and $ x_{12} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{1}   &  10.6463519313 & +  0.12 x_{9} & -0.44 x_{10} & +  0.23 x_{15} & +  3.12 x_{3} & -0.23 x_{12} & -4.16 x_{6} & -0.29 x_{13} & -5.64 x_{8}\\
 x_{2}   &  29.0128755365 & +  0.22 x_{9} & -1.10 x_{10} & +  0.47 x_{15} & +  6.53 x_{3} & -0.64 x_{12} & -10.75 x_{6} & -0.67 x_{13} & -14.49 x_{8}\\
 x_{11}   &  263.778540773 & +  2.60 x_{9} & -10.46 x_{10} & +  4.85 x_{15} & + 59.45 x_{3} & -5.30 x_{12} & -97.55 x_{6} & -4.94 x_{13} & -145.64 x_{8}\\
 x_{5}   &  25.6472103004 & +  0.24 x_{9} & -1.14 x_{10} & +  0.50 x_{15} & +  7.62 x_{3} & -0.57 x_{12} & -10.35 x_{6} & -0.60 x_{13} & -14.74 x_{8}\\
 x_{7}   &  38.8755364807 & +  0.38 x_{9} & -1.50 x_{10} & +  0.60 x_{15} & +  8.19 x_{3} & -0.84 x_{12} & -13.93 x_{6} & -0.82 x_{13} & -19.56 x_{8}\\
 x_{14}   &  118.810300429 & +  0.84 x_{9} & -4.62 x_{10} & +  1.64 x_{15} & + 25.03 x_{3} & -1.98 x_{12} & -39.33 x_{6} & -1.47 x_{13} & -69.33 x_{8}\\
 x_{4}   &  30.3442060086 & +  0.28 x_{9} & -1.12 x_{10} & +  0.52 x_{15} & +  6.36 x_{3} & -0.67 x_{12} & -11.15 x_{6} & -0.61 x_{13} & -15.59 x_{8}\\
 x_{16}   &  5.01030042918 & -0.46 x_{9} & +  1.68 x_{10} & -0.66 x_{15} & -12.97 x_{3} & +  0.22 x_{12} & +  2.97 x_{6} & +  0.93 x_{13} & + 10.47 x_{8}\\
\hline
z    &  281.231759657 & +  2.61 x_{9} & -10.19 x_{10} & +  4.16 x_{15} & + 51.58 x_{3} & -6.14 x_{12} & -99.81 x_{6} & -5.46 x_{13} & -138.22 x_{8}\\
\end{array}\]


 $ x_{3} $ enters and $ x_{16} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{1}   &  11.8496195832 & +  0.01 x_{9} & -0.03 x_{10} & +  0.08 x_{15} & -0.24 x_{16} & -0.17 x_{12} & -3.45 x_{6} & -0.07 x_{13} & -3.13 x_{8}\\
 x_{2}   &  31.5354283824 & -0.01 x_{9} & -0.26 x_{10} & +  0.14 x_{15} & -0.50 x_{16} & -0.52 x_{12} & -9.25 x_{6} & -0.21 x_{13} & -9.22 x_{8}\\
 x_{11}   &  286.735097585 & +  0.50 x_{9} & -2.74 x_{10} & +  1.84 x_{15} & -4.58 x_{16} & -4.28 x_{12} & -83.95 x_{6} & -0.69 x_{13} & -97.66 x_{8}\\
 x_{5}   &  28.5890836917 & -0.03 x_{9} & -0.16 x_{10} & +  0.11 x_{15} & -0.59 x_{16} & -0.44 x_{12} & -8.60 x_{6} & -0.06 x_{13} & -8.59 x_{8}\\
 x_{7}   &  42.0378432021 & +  0.09 x_{9} & -0.44 x_{10} & +  0.19 x_{15} & -0.63 x_{16} & -0.70 x_{12} & -12.05 x_{6} & -0.23 x_{13} & -12.95 x_{8}\\
 x_{14}   &  128.474561694 & -0.04 x_{9} & -1.37 x_{10} & +  0.38 x_{15} & -1.93 x_{16} & -1.55 x_{12} & -33.61 x_{6} & +  0.32 x_{13} & -49.13 x_{8}\\
 x_{4}   &  32.8004631161 & +  0.06 x_{9} & -0.29 x_{10} & +  0.20 x_{15} & -0.49 x_{16} & -0.56 x_{12} & -9.70 x_{6} & -0.16 x_{13} & -10.46 x_{8}\\
 x_{3}   &  0.38617267615 & -0.04 x_{9} & +  0.13 x_{10} & -0.05 x_{15} & -0.08 x_{16} & +  0.02 x_{12} & +  0.23 x_{6} & +  0.07 x_{13} & +  0.81 x_{8}\\
\hline
z    &  301.150314257 & +  0.78 x_{9} & -3.49 x_{10} & +  1.56 x_{15} & -3.98 x_{16} & -5.25 x_{12} & -88.02 x_{6} & -1.77 x_{13} & -96.59 x_{8}\\
\end{array}\]


 $ x_{9} $ enters and $ x_{3} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{1}   &  11.9728379644 & -0.32 x_{3} & +  0.01 x_{10} & +  0.06 x_{15} & -0.26 x_{16} & -0.17 x_{12} & -3.38 x_{6} & -0.05 x_{13} & -2.87 x_{8}\\
 x_{2}   &  31.4061817047 & +  0.33 x_{3} & -0.30 x_{10} & +  0.16 x_{15} & -0.48 x_{16} & -0.53 x_{12} & -9.33 x_{6} & -0.23 x_{13} & -9.49 x_{8}\\
 x_{11}   &  292.227599126 & -14.22 x_{3} & -0.90 x_{10} & +  1.12 x_{15} & -5.68 x_{16} & -4.04 x_{12} & -80.70 x_{6} & +  0.32 x_{13} & -86.18 x_{8}\\
 x_{5}   &  28.2266625039 & +  0.94 x_{3} & -0.28 x_{10} & +  0.16 x_{15} & -0.51 x_{16} & -0.46 x_{12} & -8.82 x_{6} & -0.13 x_{13} & -9.35 x_{8}\\
 x_{7}   &  43.075554168 & -2.69 x_{3} & -0.09 x_{10} & +  0.05 x_{15} & -0.84 x_{16} & -0.65 x_{12} & -11.44 x_{6} & -0.04 x_{13} & -10.78 x_{8}\\
 x_{14}   &  128.014361536 & +  1.19 x_{3} & -1.52 x_{10} & +  0.44 x_{15} & -1.84 x_{16} & -1.57 x_{12} & -33.88 x_{6} & +  0.23 x_{13} & -50.09 x_{8}\\
 x_{4}   &  33.458632532 & -1.70 x_{3} & -0.07 x_{10} & +  0.11 x_{15} & -0.62 x_{16} & -0.53 x_{12} & -9.31 x_{6} & -0.04 x_{13} & -9.09 x_{8}\\
 x_{9}   &  10.9341242585 & -28.31 x_{3} & +  3.68 x_{10} & -1.43 x_{15} & -2.18 x_{16} & +  0.49 x_{12} & +  6.48 x_{6} & +  2.02 x_{13} & + 22.85 x_{8}\\
\hline
z    &  309.732438339 & -22.22 x_{3} & -0.61 x_{10} & +  0.43 x_{15} & -5.69 x_{16} & -4.87 x_{12} & -82.93 x_{6} & -0.19 x_{13} & -78.65 x_{8}\\
\end{array}\]


 $ x_{15} $ enters and $ x_{9} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{1}   &  12.4261400829 & -1.49 x_{3} & +  0.16 x_{10} & -0.04 x_{9} & -0.36 x_{16} & -0.15 x_{12} & -3.11 x_{6} & +  0.04 x_{13} & -1.92 x_{8}\\
 x_{2}   &  32.6205542221 & -2.81 x_{3} & +  0.11 x_{10} & -0.11 x_{9} & -0.72 x_{16} & -0.48 x_{12} & -8.61 x_{6} & -0.01 x_{13} & -6.95 x_{8}\\
 x_{11}   &  300.814095571 & -36.46 x_{3} & +  1.99 x_{10} & -0.79 x_{9} & -7.39 x_{16} & -3.65 x_{12} & -75.62 x_{6} & +  1.91 x_{13} & -68.24 x_{8}\\
 x_{5}   &  29.4505782239 & -2.23 x_{3} & +  0.13 x_{10} & -0.11 x_{9} & -0.76 x_{16} & -0.40 x_{12} & -8.09 x_{6} & +  0.10 x_{13} & -6.79 x_{8}\\
 x_{7}   &  43.4835260746 & -3.74 x_{3} & +  0.04 x_{10} & -0.04 x_{9} & -0.92 x_{16} & -0.63 x_{12} & -11.20 x_{6} & +  0.03 x_{13} & -9.93 x_{8}\\
 x_{14}   &  131.375954615 & -7.51 x_{3} & -0.39 x_{10} & -0.31 x_{9} & -2.51 x_{16} & -1.42 x_{12} & -31.89 x_{6} & +  0.85 x_{13} & -43.07 x_{8}\\
 x_{4}   &  34.3246781584 & -3.95 x_{3} & +  0.22 x_{10} & -0.08 x_{9} & -0.79 x_{16} & -0.49 x_{12} & -8.80 x_{6} & +  0.12 x_{13} & -7.28 x_{8}\\
 x_{15}   &  7.64171939777 & -19.79 x_{3} & +  2.57 x_{10} & -0.70 x_{9} & -1.53 x_{16} & +  0.34 x_{12} & +  4.53 x_{6} & +  1.41 x_{13} & + 15.97 x_{8}\\
\hline
z    &  313.055858608 & -30.83 x_{3} & +  0.51 x_{10} & -0.30 x_{9} & -6.35 x_{16} & -4.72 x_{12} & -80.97 x_{6} & +  0.43 x_{13} & -71.70 x_{8}\\
\end{array}\]


 $ x_{10} $ enters and $ x_{14} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{1}   &  66.3671309192 & -4.58 x_{3} & -0.41 x_{14} & -0.17 x_{9} & -1.38 x_{16} & -0.73 x_{12} & -16.20 x_{6} & +  0.39 x_{13} & -19.61 x_{8}\\
 x_{2}   &  69.435097493 & -4.92 x_{3} & -0.28 x_{14} & -0.20 x_{9} & -1.42 x_{16} & -0.87 x_{12} & -17.55 x_{6} & +  0.23 x_{13} & -19.02 x_{8}\\
 x_{11}   &  967.720891365 & -74.60 x_{3} & -5.08 x_{14} & -2.35 x_{9} & -20.12 x_{16} & -10.84 x_{12} & -237.50 x_{6} & +  6.25 x_{13} & -286.85 x_{8}\\
 x_{5}   &  74.4623955432 & -4.81 x_{3} & -0.34 x_{14} & -0.22 x_{9} & -1.62 x_{16} & -0.89 x_{12} & -19.02 x_{6} & +  0.39 x_{13} & -21.55 x_{8}\\
 x_{7}   &  58.4874651811 & -4.60 x_{3} & -0.11 x_{14} & -0.07 x_{9} & -1.21 x_{16} & -0.80 x_{12} & -14.84 x_{6} & +  0.13 x_{13} & -14.85 x_{8}\\
 x_{10}   &  335.429526462 & -19.18 x_{3} & -2.55 x_{14} & -0.78 x_{9} & -6.40 x_{16} & -3.62 x_{12} & -81.42 x_{6} & +  2.18 x_{13} & -109.95 x_{8}\\
 x_{4}   &  107.368245125 & -8.12 x_{3} & -0.56 x_{14} & -0.25 x_{9} & -2.19 x_{16} & -1.28 x_{12} & -26.53 x_{6} & +  0.60 x_{13} & -31.22 x_{8}\\
 x_{15}   &  869.306963788 & -69.07 x_{3} & -6.56 x_{14} & -2.72 x_{9} & -17.97 x_{16} & -8.95 x_{12} & -204.63 x_{6} & +  7.02 x_{13} & -266.48 x_{8}\\
\hline
z    &  484.320334262 & -40.62 x_{3} & -1.30 x_{14} & -0.70 x_{9} & -9.62 x_{16} & -6.57 x_{12} & -122.54 x_{6} & +  1.54 x_{13} & -127.84 x_{8}\\
\end{array}\]


 $ x_{13} $ enters and Unbounded Dictionary!


 $ x_{13} $ enters and Unbounded Dictionary!
\end{document}
